Theorems · Theorem · ring theory

Module.Baer.ExtensionOf.le_max

∀ {R : Type u} [inst : Ring R] {Q : Type v} [inst_1 : AddCommGroup Q] [inst_2 : Module R Q] {M : Type u_1}
  {N : Type u_2} [inst_3 : AddCommGroup M] [inst_4 : AddCommGroup N] [inst_5 : Module R M] [inst_6 : Module R N]
  {i : M →ₗ[R] N} {f : M →ₗ[R] Q} {c : Set (Module.Baer.ExtensionOf i f)} (hchain : IsChain (fun x1 x2 => x1 ≤ x2) c)
  (hnonempty : c.Nonempty), ∀ a ∈ c, a ≤ Module.Baer.ExtensionOf.max hchain hnonempty

Defined in

Mathlib.Algebra.Module.Injective

Cited by

1 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddCommGroupAddCommGroupModuleModule